Unique recovery of piecewise analytic density and stiffness tensor from the elastic-wave Dirichlet-to-Neumann map

TL;DR

This paper proves that the piecewise analytic density and stiffness tensor of a 3D elastic medium can be uniquely reconstructed from boundary measurements, even with limited prior knowledge of the medium's symmetry and interfaces.

Contribution

It establishes new global uniqueness results for recovering elastic parameters from the Dirichlet-to-Neumann map, including cases with unknown interfaces and various symmetry assumptions.

Findings

Unique recovery of piecewise analytic density and stiffness tensor.

Global uniqueness results under symmetry and interface assumptions.

Determination of domain partition as a subanalytic set.

Abstract

We study the recovery of piecewise analytic density and stiffness tensor of a three-dimensional domain from the local dynamical Dirichlet-to-Neumann map. We give global uniqueness results if the medium is transversely isotropic with known axis of symmetry or orthorhombic with known symmetry planes on each subdomain. We also obtain uniqueness of a fully anisotropic stiffness tensor, assuming that it is piecewise constant and that the interfaces which separate the subdomains have curved portions. The domain partition need not to be known. Precisely, we show that a domain partition consisting of subanalytic sets is simultaneously uniquely determined.